Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.HasPullbacks
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → PropP has pullbacks if for every f satisfying P, pullbacks of arbitrary morphisms along f
exist.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.coveragestatement and proof · cited by 2
- CategoryTheory.MorphismProperty.HasPullbacks.hasPullbackstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.grothendieckTopologystatement and proof · cited by 1
- CategoryTheory.MorphismProperty.HasPullbacks.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.HasPullbacks.recOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.coverage_toPrecoveragestatement and proof · cited by 0
- CategoryTheory.MorphismProperty.hasPullbackstatement · cited by 0
- CategoryTheory.MorphismProperty.hasPullbacksAgainst_top_iffstatement and proof · cited by 0